Problem: What do the following two equations represent? $-x+y = 5$ $-2x+2y = 4$
Solution: Putting the first equation in $y = mx + b$ form gives: $-x+y = 5$ $y = x+5$ Putting the second equation in $y = mx + b$ form gives: $-2x+2y = 4$ $2y = 2x+4$ $y = 1x + 2$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.